18.) Jupiter has a mass of 1.9 x 1027kg and its moon Europa has a mass of 4.8 x 10kg. The
magnitude of the gravitational force between them is 1.4 x1022N. What is the distance between
them?

The free-fall acceleration on Mars is 3.71 m/s²

Given :

gravitational force acting on the robot is 504.6 N

F= 504.6 N

mass of the robot  = 136 kg

a = F/ m

= 504.6/ 136 =3.71 m/s²

The free-fall acceleration on Mars is 3.71 m/s²

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The velocity of the stone just before it strikes the ground is 39.6 m/s.

Velocity can be defined as the rate of change of displacement.

To calculate the velocity at which the bstone strikes the ground, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for v

Hence, the velocity is 39.6 m/s.

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Answer:44.3

Explanation:

XXX high shutter speed is the kind of setting that will help emphasise motion blur.

Motion blur is the appearance of moving objects streaming across a frame or sequence of frames, such as in a video or animation. When there is rapid movement or a long exposure, it occurs when the image being recorded changes throughout the course of one exposure. In both photography and video, motion blur is a result of the shutter speed, or how long the iris of the camera is open and exposed. When exposed for a longer period of time with a slower shutter speed than they would with a faster one, moving objects move further and fuzz more. Both photography and video can capture the motion blur effect, although they do it in somewhat different ways and for slightly different reasons. On the other hand, the effect itself is essentially the same in both mediums.

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The maximum force that the spring exerts on the mass is 3.847N if spring is in simple harmonic motion.

In mechanics and physical science,simple harmonic motion (some of the time shortened SHM) is an exceptional kind of occasional movement of a body coming about because of a powerful harmony between an inertial power

We have kinetic energy in Simple harmonic motion =(1/2)mω²A² where m is the mass,ω is the angular frequency and A is the amplitude of the body.

Now,we need to find the force exerted by spring which is given by formula =ma=mω²A .So,we need to find the mω².

We have kinetic energy as =4.04J

So,on putting the values we get

=>4.04=(1/2)×m×ω²×(0.21)²

=>4.04×2 = m×ω²×(0.21)²

=>8.08 =m×ω²×0.441

=>mω²=8.08/0.441

=>mω²=18.32kg/sec²

Now,we know that force is given by formula=mω²x where x is the maximum amplitude of spring.Here value of x is 0.21m.

So,F=mω²x

=>F=18.32×0.21

=>F=3.847N

Hence,maximum force is 3.847N.

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The average speed of the car is 35.6m/s

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction. It is measured in meter per second

Therefore average speed = total distance / total time taken

The total distance here is 500+ 500= 1000km = 1×10⁶m

the time taken for the first journey = 500×1000/35= 14285.71 seconds

the time taken for traveling back = 500000/43= 11627.91 seconds

total time taken = 14285.71 + 11627.91 = 25913.62seconds

therefore average speed = 1000000/25913.62

= 35.6m/s

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If at noon , the ship A is 170 km west of ship B , then the distance between the ships changing at 4:00 p.m. is 28.85 kmph   .

The ship A is 170 km west of ship B and

ship A is sailing east at the speed of  40 km/h ;

ship B is sailing north at the speed of  25 km/h ;

let us consider "x" and "y" as initial position of ships A and B ;

let the distance between ship A and "x" = x ;

let the distance between ship B and "x" = y ;

let the distance between ship A and ship B = z ;

By using Pythagoras Theorem ;  z² = x² + y²  ;

differentiating w.r.t. "t" ,

we get ;

2z*dz/dt = 2x*dx/dt + 2y*dy/dt

on Dividing equation by 2 on both sides ;

z*dz/dt = x*dx/dt + y*dy/dt     .....equation(1)

given ; dx/dt = 40 km/hr  and   dy/dt = 25 km/hr

Now , When t = 4 hours,

since at noon ; the ship A is west of Ship B ;

we get ;   x = 40*4 = 170 - 160 = 10  ;  y = 25*4 = 100 and

z = √(x² + y²)  , putting the values of x and y ,

we get ;

z = √(x² + y²)  ;

z = √(10² + 100²)  ;

substituting the values ; we get

z = √100+10000

z = √10100

z = 100.49

putting the values of x , y and z , in equation(1) ,

we get ;

100.49*dz/dt = 10*40 + 100*25 ;

100.49*dz/dt = 400 + 2500

100.49*dz/dt = 2900

dz/dt = 2900/100.49

dz/dt = 28.85 kmph ;

Therefore , The distance between the ships is changing at 4:00 p.m. is 28.85 kmph .

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The wavelength of visible light compare to radio waves in the sense that visible light waves have a shorter wavelength than radio waves.

The wavelength is described as the spatial period of a periodic wave which is the distance over which the wave's shape repeats.

Radio waves are electromagnetic waves that are produced by man with an oscillating circuit.

Radio waves are used in broadcasting, the waves used in television are those of shorter wavelength and those of radio are those of longer wavelength.

Longer radions are reflected in the ionosphere and can be detected in antennas which is located at great distances from the emitting source. The medium waves are less reflected in the ionosphere, due to their large wavelength they can overcome obstacles, so they can travel great distances.

It is known that the visible radiation waves have a wavelength between approximately 400 and 700 nanometers, the radio waves range from 1 centimeter to 1 km, so they have longer wavelengths than the waves belonging to the visible spectrum.

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If a thin layer with an index of refraction of 1.4 and a thickness of 280 nm coats a glass plate with an index of refraction of 1.65, the minimum wavelength of the reflected light is 182 nm.

When a waveform signal travels across space or down a wire, its wavelength is the distance between two identical locations (adjacent crests) in adjacent cycles. The standard units of measurement for this length in wireless systems are meters (m), centimeters (cm), or millimeters (mm) (mm).

Light is coming from a medium with a lower refractive index (n 1 = 1.50) into a medium with a higher index (n 2 = 1.60), so the net path difference in the reflected rays from the two interfaces will be equal to 2t (where t is the thickness of the thin film), because when that happens, light will enter the higher index medium.

When light travels from air to a thin film, the reflected ray's path shift equals 2; when it travels from a thin film to glass, the reflected ray's path shift equals 2′ /2+2t for constructive interference; 2t=m or 2t=m/n 1 where is the wavelength in the thin film, =546nm (given) wavelength in vacuum, and m=0 (minimum); thus, t

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The uncertainty in position if the velocity is 100.0 mi/h 1.0 % is 5.19 x 10-36 m.

Velocity is a vector quantity that describes the rate and direction of an object's motion. It is typically expressed as the magnitude of the speed of an object in a given direction. Velocity can be determined by measuring the displacement of an object over a certain amount of time. It is an important concept in physics, as it is used to describe the motion of objects. Velocity is closely related to other physical quantities such as acceleration, momentum, and force.

The uncertainty in position can be determined using Heisenberg's Uncertainty Principle. This states that the product of the uncertainty in position and the uncertainty in momentum must be greater than or equal to the Planck constant (h) divided by 4π. The momentum of the electron is equal to its mass multiplied by its velocity. Thus, the uncertainty in position is equal to (h)/(4πmv), where m is the mass of the electron and v is the velocity. In this case, this would be equal to

(6.626 x 10-34 Js)/(4π x 9.10939 x 10-31 kg x (100.0 mi/h x 1609.34 m/mi))

=5.19 x 10-36 m.

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Answer:

i) E1 = -13.6/1² = -13.6eV

E2 = -13.6/2² = -3.4 eV

E3 = -13.6/3² = -1.51 eV

E4 = -13.6/4² = -0.85 eV

E5 = -13.6/5² = -0.544 eV

E6 = -13.6/6² = -0.377 eV

E∞ = 0

ii) Lyman series obtained when there is electron transition from n = 2,3,4,5,6... to n1=1

Baler series obtained when there is a transition from n = 3,4,5,6.. to n1 = 2

iii) E ( ionisation) = E∞ - E1 = 0 - (- 13.6) = 13.6 eV

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parallel processing perceiving the color, motion, and form of a bird in flight illustrates.

Option a is correct.

According to the trichromatic theory, our ability to perceive red, green, and blue hues as well as how they affect our cerebral activity are both explained by cones (Like a projection T.V.). Consequently, the precise colour we see is determined by the proportion of each colour to the others.

The three kinds of cone receptors that are responsible for colour vision are the foundation of the trichromatic hypothesis of colour vision. Beginning in the 18th century, this hypothesis has a very long history.

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a. True If two vectors are perpendicular to each other, their cross product must be zero.

The vector is always equal to its cross-vector product. A line that is perpendicular to another line will create an angle of 900 degrees between them. As a result, even if two provided vectors are perpendicular, their cross product does not equal zero, but their dot product does.

A 90 degree angle is created between two vectors when they are perpendicular to one another. As we all know, the cross product of two vectors is equal to the product of the magnitudes of the vectors and the sine of the angle between them.

The dot product of two vectors that are perpendicular to one another is equal to zero.

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A batter is struck with a baseball that weighs 0.15 kg at a speed exceeding 32.0 m/s. When a 0.94 kilogram bat. After a collision, the baseball's final speed was 24 m/s.

The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and indeed the basic unit pf distance are combined to form the Special name of speed.

Speed indicates how quickly thing or an individual are moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.

Mass of baseball, m=0.15kg,

Mass of bat, M=1.4kg,

Initial speed of baseball, u=-32 m/s,

Initial speed of bat, U=41 m/s

Final speed of bat, V=35 m/s,

Linear momentum, mu+MU = mv+MV

(0.15" " kg×-32" " m/s)+(1.4" " kg×41" " m/s)

=(0.15" " kg ×v)+(1.4" " kg×35" " m/s)

-4.8+57.4 = 0.15v+49

0.15v = 3.6

v=(3.6)/(0.15)

v=24m/s

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A BTU is defined as the amount of energy required to raise the temperature of one lb of water by one-degree celsius is False.

A British thermal unit is a measure of the amount of heat in a fuel or energy source. This is the amount of heat required to raise the temperature of 1 pound of liquid water by 1 degree Fahrenheit, the temperature at which water reaches its maximum density.

BTU is the amount of energy required to raise the temperature of 1 pound of water to 1 degree Fahrenheit above sea level. Technically, this measurement refers to the amount of energy required for this process when water is at its maximum density.

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The two parakeets sitting on the swing with a combined center of mass 16.0 cm below the pivot swings with a frequency of 1.21Hz.

Given the data in the question

Length of pendulum; L=16.0cm =0.16m

Frequency; f=

Using the simple pendulum equation of time:

T2π = √L/9 -------let this be equation 1

Where T is the period of time, L is the length of the pendulum and g is the acceleration due to gravity(9.8m/s² ).

Also formula for Frequency:

f=1/T ------------let this be equation 2

Lets substitute equation 1 into equation 2

f = 1/2π√L/9

f = 1/2π√9/L

We substitute or values into the equation

f=1/2π√[9.8/0.16]

f=1/2π√[57.647-2]

f=1/2π*7.59256s

f=1.21 hZ

Therefore, the two parakeets sitting on the swing with a combined center of mass 16.0 cm below the pivot swings with a frequency of 1.21Hz.

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if Betelgeuse were to radiate all of its energy at the peak-intensity wavelength, how many photons.

What is energy?

Energy, which is observable in the execution of labour as well as in the form of heat and light, is the quantitative quality that is transferred to a body or to a physical system in physics. It is a mechanically accepted quantity.

a )

Radius of the sun = .69645 x 10⁹ m .

600 times = 600 x .69645 x 10⁹ m

= 4.1787 x 10¹¹ m .

surface area A = 4π (4.1787 x 10¹¹)²

= 219.317 x 10²²

energy radiated E = σ A Τ⁴

= 5.67 x 10⁻⁸ x 219.317 x 10²² x (3000)⁴

= 100695 x 10²⁶ J

To know the wavelength of photon emitted

[tex]\begin{aligned}& \lambda_m T=b \\& \lambda_m=\frac{b}{T}\end{aligned}[/tex]

= 2.89777 x 10⁻³ / 3000

= 966 nm

= 1275 /966 eV

1.32 x 1.6 x 10⁻¹⁹ J

= 2.112 x 10⁻¹⁹ J

No of photons radiated = 100695 x 10²⁶ / 2.112 x 10⁻¹⁹

= 47677.5 x 10⁴⁵

= .476 x 10⁵⁰ .

b )

energy radiated by our sun per second

E₂ = σ A 5800⁴

energy radiated by Betelgeuse per second

E₁ = σ  x 600²A x  3000⁴

E₁ / E₂  = σ  x 600²A x  3000⁴ / σ A 5800⁴

= 36 X 10⁴ x 3⁴ x 10¹² / 58⁴ x 10⁸

= 25.76 x 10⁸ x 10⁻⁵

= 25760 times .

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Complete Question

The red giant Betelgeuse has a surface temperature of 3000 K and is 600 times the diameter of our sun. (If our sun were that large, we would be inside it!) Assume that it radiates like an ideal blackbody.a) If Betelgeuse were to radiate all of its energy at the peak-intensity wavelength, how many photons per second would it radiate?b) Find the ratio of the power radiated by Betelgeuse to the power radiated by our sun (at 5800 K).

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A satellite with mass m orbits a planet in time t. Since a satellite's mass has no bearing on how long it takes to orbit a planet, if the satellite had two times as much mass, the time it would take to do so would be t.

An object in space known as a satellite orbit or revolves around a larger object. Satellites can be either natural (like the moon circling the Earth) or manmade (such as the International Space Station orbiting the Earth).

A deliberately built body (with special purposes) that has been launched into orbit using rockets or other propulsion systems is known as an artificial satellite.

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We can see the star Sirius and its companion, the pup, moving around each other. careful measurement of this motion can provide: the masses of both stars in the system.

The required mass in kg when the power output, time, height are given is 7.63 kg.

We know that, the formula for power output for a motor is

Power P = (m* g*h)/t

where,

m is the mass in kg

g is the acceleration due to gravity in m/s²

h is the height in m

t is the time in sec

Given that,

P = 187 W

g = 9.8 m/s²

h = 13 m

t = 5.2 s

m = ?

Making m as subject in the above equation, we get,

m = (P* t)/(g* h) = (187* 5.2)/(9.8* 13) = 7.63 kg.

Thus, the required mass in kg is 7.63 kg.

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In actuality, an object's velocity rises by 9.8 m/s2, thus it reaches 9.8 m/s by the time it begins to fall.By the time it has been falling for 2 seconds (9.8 m/s plus 9.8 m/s), it is moving at 19.6 m/s, and so on.

Gravity will cause any object to move forward at a rate of 32 feet per second each second.

Choose the length of the item's descent.We'll use an 8-second sample as our example.Its final free fall speed (just before it touches the earth) is calculated using equation v = v0 + gt = 0 + 9.80665 * 8 and equals 78.45 m/s.Find the free-falling distance using the formula s = (1/2)gt2: 0.5 * 9.80665 * 82 = 313.8 meters

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Answer:

ΔL = L * 1.9E-5 * ΔT

ΔA = A * 2 * 1.9E-5 * ΔT

ΔA = .6 * 3.8E-5 * 1.5E4 mm = .34 mm

New area = 600.34 mm

Note: (L + ΔL)^2 = L + 2 L ΔL + ΔL^2       where ΔL is a small quantity

(L + ΔL)^2 - L^2 = 2 L ΔL = L ΔA

where the coefficient of area expansivity is twice that of linear expansivity

Answer:C car

Explanation:

The total mass of the galaxy within a radius of 5 kpc is approximately 3.25 billion solar masses.

A galaxy is a system of stars, remnants of stars, interstellar gas, dust, dark matter, bound together by gravity.

By using the equations of Newtonian mechanics, the total mass of the galaxy can be calculated by combining the mass of the stars, gas, dust, and dark matter within the 5 kpc radius.

The total mass of a galaxy within a radius of 5 kpc can be calculated using the equation:

Mass = 2.3 x 10⁶ x (5 kpc)² x (1 solar mass/pc³)

Mass = 3.25 billion solar masses.

This calculation provided an approximate total mass for the galaxy, which is estimated to be 3.5 billion solar masses located within 5 kpc of the center.

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The gauge pressure of the air in the tires when its temperature rises to 27.0 degrees celsius and its volume increases to 1.67 x 10-2 m3 is 175 kPa.

Temperature is a measure of the average kinetic energy of the particles in a system. It is measured using a thermometer and is typically expressed in units of degrees Celsius (°C), Fahrenheit (°F), or Kelvin (K). Temperature is an important factor in determining the state of matter, as well as the rate of chemical reactions and the motion of particles within a system.

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. Therefore, we can rearrange the equation to solve for P:
P = (nRT) / V
We can plug in the given values to find the initial pressure:
P = [(1.67 x 10-2 m3)(1.01 x 105 pa) / (1.64 x 10-2 m3)] / (0.00 + 273.15)
P = 165 kPa
Now, we can find the new pressure when the temperature rises to 27.0 degrees celsius and the volume increases to 1.67 x 10-2 m3:
P = [(1.67 x 10-2 m3)(1.01 x 105 pa) / (1.67 x 10-2 m3)] / (27.0 + 273.15)

P = 175 kPa
Therefore, the gauge pressure of the air in the tires when its temperature rises to 27.0 degrees celsius and its volume increases to 1.67 x 10-2 m3 is 175 kPa.

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The flow rate of the water in the pipe is given by Q=Av

where

Q is the flow rate

A is the cross-sectional area of the pipe

v is the speed of the water

with the help of question,

,

Q=1.20m3/s

the radius of the pipe is

r = 0.160 m

So, the cross-sectional area is

;

;A=πr^2 where r=0.160mm

=π(0.160×0.160)2=0.0256m

So we can re-arrange the equation to find the speed of the water:

;v=Q/A=1.20m3/s/0.0256

=4687.5m3

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The average frequency of the two forks will be 457 Hz.

Frequency:

In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time. When a body in periodic motion goes through a series of events or positions before returning to its initial state, it is said to have experienced one cycle or one vibration.

Average Frequency;

Mathematically,

                           [tex]f_{Avg}=\frac{f_{1}+f_{2} }{2}[/tex]

Given,

         [tex]f_{1} = 454 Hz[/tex]

         [tex]f_{2}=460 Hz\\[/tex]

Using the Average frequency formula,

                         [tex]f_{Avg}=\frac{f_{1}+f_{2} }{2}= \frac{454+460}{2}[/tex]

                        [tex]f_{Avg}=\frac{914}{2}[/tex]

                         [tex]f_{Avg}=457Hz[/tex]                       

Hence,

         The average frequency of the two forks will be 457 Hz.

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The accuracy of the non-relativistic momentum formula is 5.32 10 3 keV.

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A day would be 85 min long if the earth were rotating so fast that objects at the equator were apparently weightless.

At the equator, the centrifugal force and gravitational force must be equal in order to feel weightless.

[tex]\frac{mv^{2} }{R} = mg[/tex]

∴ [tex]v = \sqrt{gR}[/tex]

[tex]\frac{2\pi r}{T} = \sqrt{gR}[/tex]

[tex]{T} = \frac{2\pi r}\sqrt{gR}[/tex]

[tex]T= \frac{2 \pi (64000)}{\sqrt{9.8(64000)} }[/tex]

T = 5.07×10³s

∴T = 85 min.

While Earth rotates on its axis from west to east, the Sun and Moon appear to move across the sky from east to west. The term "rotation" in science refers to the Earth's rotation about its axis. The axis has an angle of 23 1/2° and is parallel to the Earth's orbital plane. The fact that the northern and southern hemispheres tilt away from the Sun suggests that the Earth's axis is inclined. The Earth revolves, dividing it into a lit up and dark half, resulting in day and night. You can tell which way the Earth is rotating depending on your point of view. When looking downward from the North Pole, Earth turns anticlockwise. When seen from the south pole, however, the world revolves anticlockwise.

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First I would ask

how much their budget is for one year. Next I would ask how they are going to have more clean energy. Other questions I would ask are where will you install the solar farms, will the farms impact local businesses and how much dirty energy they want to get out of the atmosphere